Docstoc

Contents at a Glance

Document Sample
Contents at a Glance Powered By Docstoc
					                       Contents at a Glance
Introduction .............................................................................1
Part I: Back to Basics with Basic Math......................................5
Chapter 1: We’ve Got Your Numbers...................................................................................................7
Chapter 2: Smooth Operators: Working with the Big Four Operations ........................................23




                                                                                        AL
Chapter 3: Getting Down with Negative Numbers...........................................................................37
Chapter 4: It’s Just an Expression......................................................................................................49




                                                                                  RI
Chapter 5: Dividing Attention: Divisibility, Factors, and Multiples ...............................................69




                                                                           TE
Part II: Slicing Things Up: Fractions, Decimals, and Percents ....89
Chapter 6: Fractions Are a Piece of Cake..........................................................................................91


                                                                MA
Chapter 7: Fractions and the Big Four ............................................................................................107
Chapter 8: Getting to the Point with Decimals...............................................................................141
Chapter 9: Playing the Percentages.................................................................................................163
                                                          D
Part III: A Giant Step Forward: Intermediate Topics ................175
                                                   TE

Chapter 10: Seeking a Higher Power through Scientific Notation ...............................................177
Chapter 11: Weighty Questions on Weights and Measures ..........................................................187
Chapter 12: Shaping Up with Geometry..........................................................................................201
                                         GH



Chapter 13: Getting Graphic: Cartesian Graphs.............................................................................221

Part IV: The X Factor: Introducing Algebra .............................233
                                   RI




Chapter 14: Expressing Yourself with Algebraic Expressions......................................................235
Chapter 15: Finding the Right Balance: Solving Algebraic Equations .........................................255
                           PY




Part V: The Part of Tens ........................................................271
                 CO




Chapter 16: Ten Alternative Numeral and Number Systems........................................................273
Chapter 17: Ten Curious Types of Numbers ..................................................................................281

Index ...................................................................................287
                           Table of Contents
Introduction..............................................................................1
            About This Book ..................................................................................................................1
            Conventions Used in This Book.........................................................................................2
            Foolish Assumptions...........................................................................................................2
            How This Book Is Organized ..............................................................................................2
                  Part I: Back to Basics with Basic Math....................................................................2
                  Part II: Slicing Things Up: Fractions, Decimals, and Percents..............................3
                  Part III: A Giant Step Forward: Intermediate Topics..............................................3
                  Part IV: The X Factor: Introducing Algebra ............................................................3
                  Part V: The Part of Tens ............................................................................................3
            Icons Used in This Book .....................................................................................................4
            Where to Go from Here .......................................................................................................4


Part I: Back to Basics with Basic Math ......................................5
     Chapter 1: We’ve Got Your Numbers .............................................................................7
            Getting in Place with Numbers and Digits........................................................................7
            Rollover: Rounding Numbers Up and Down ..................................................................10
            Using the Number Line with the Big Four ......................................................................12
            The Column Lineup: Adding and Subtracting................................................................14
            Multiplying Multiple Digits ...............................................................................................15
            Cycling through Long Division.........................................................................................17
            Solutions to We’ve Got Your Numbers............................................................................19

     Chapter 2: Smooth Operators: Working with the Big Four Operations.................23
            Switching Things Up with Inverse Operations and the Commutative Property .......23
            Getting with the In-Group: Parentheses and the Associative Property......................27
            Becoming Unbalanced: Inequalities ................................................................................30
            Special Times: Powers and Square Roots.......................................................................32
            Answers to Problems in Smooth Operators...................................................................34

     Chapter 3: Getting Down with Negative Numbers ...................................................37
            Understanding Where Negative Numbers Come From.................................................37
            Sign-Switching: Understanding Negation and Absolute Value .....................................39
            Adding with Negative Numbers .......................................................................................40
            Subtracting with Negative Numbers ...............................................................................42
            Comparing Signs of the Times (And Division) of Negative Numbers .........................43
            Answers to Problems in Getting Down with Negative Numbers .................................45
x   Basic Math & Pre-Algebra Workbook For Dummies

            Chapter 4: It’s Just an Expression................................................................................49
                   Evaluating Expressions with Addition and Subtraction ...............................................49
                   Evaluating Expressions with Multiplication and Division ............................................51
                   Making Sense of Mixed-Operator Expressions ..............................................................52
                   Handling Powers Responsibly .........................................................................................53
                   Prioritizing Parentheses ...................................................................................................54
                   Pulling Apart Parentheses and Powers...........................................................................56
                   Figuring Out Nested Parentheses ....................................................................................57
                   Bringing It All Together: The Order of Operations........................................................59
                   Solutions to It’s Just an Expression.................................................................................60

            Chapter 5: Dividing Attention: Divisibility, Factors, and Multiples .......................69
                   Checking for Leftovers: Divisibility Tests.......................................................................69
                   Understanding Factors and Multiples.............................................................................72
                   One Number, Indivisible: Identifying Prime (And Composite) Numbers ...................73
                   Generating a Number’s Factors .......................................................................................75
                   Decomposing a Number into Its Prime Factors.............................................................77
                   Finding the Greatest Common Factor (GCF)..................................................................79
                   Generating the Multiples of a Number............................................................................81
                   Finding the Least Common Multiple (LCM) ...................................................................82
                   Solutions to Divisibility, Factors, and Multiples ............................................................84


        Part II: Slicing Things Up: Fractions, Decimals, and Percents.....89
            Chapter 6: Fractions Are a Piece of Cake ..................................................................91
                   Getting Down the Basic Fraction Stuff ............................................................................91
                   In Mixed Company: Converting between Mixed Numbers and
                     Improper Fractions ........................................................................................................94
                   Increasing and Reducing the Terms of Fractions ..........................................................97
                   Comparing Fractions with Cross-Multiplication..........................................................100
                   Solutions to Fractions Are a Piece of Cake...................................................................102

            Chapter 7: Fractions and the Big Four.......................................................................107
                   Multiplying Fractions: A Straight Shot..........................................................................107
                   Flipping for Fraction Division.........................................................................................109
                   Reaching the Common Denominator: Adding Fractions ............................................111
                   The Other Common Denominator: Subtracting Fractions .........................................115
                   Multiplying and Dividing Mixed Numbers....................................................................118
                   Carried Away: Adding Mixed Numbers.........................................................................120
                   Borrowing from the Whole: Subtracting Mixed Numbers ..........................................123
                   Solutions to Fractions and the Big Four .......................................................................127

            Chapter 8: Getting to the Point with Decimals........................................................141
                   Getting in Place: Basic Decimal Stuff.............................................................................141
                   Knowing Simple Decimal-Fraction Conversions..........................................................144
                   A New Lineup: Adding and Subtracting Decimals .......................................................146
                   Counting Decimal Places: Multiplying Decimals .........................................................148
                   Decimal Points on the Move: Dividing Decimals .........................................................149
                   Changing Decimals to Fractions ....................................................................................151
                                                                                                    Table of Contents              xi
          Changing Fractions to Decimals ....................................................................................153
          Solutions to Getting to the Point with Decimals..........................................................155

    Chapter 9: Playing the Percentages..........................................................................163
          Converting Percents to Decimals ..................................................................................163
          Changing Decimals to Percents .....................................................................................165
          Switching from Percents to Fractions...........................................................................166
          Converting Fractions to Percents..................................................................................167
          Mixing Things Up with the Percent Circle....................................................................169
          Solutions to Playing the Percentages............................................................................172


Part III: A Giant Step Forward: Intermediate Topics.................175
    Chapter 10: Seeking a Higher Power through Scientific Notation .....................177
          On the Count of Zero: Understanding Powers of Ten .................................................177
          Exponential Arithmetic: Multiplying and Dividing Powers of Ten ............................180
          Representing Numbers in Scientific Notation..............................................................181
          Multiplying and Dividing with Scientific Notation.......................................................182
          Answers to Problems in Seeking a Higher Power through Scientific Notation .......184

    Chapter 11: Weighty Questions on Weights and Measures .................................187
          The Basics of the English System ..................................................................................187
          Going International with the Metric System ................................................................190
          Converting between English and Metric Units ............................................................193
          Answers to Problems in Weighty Questions on Weights and Measures ..................195

    Chapter 12: Shaping Up with Geometry....................................................................201
          Getting in Shape: Polygon (And Nonpolygon) Basics.................................................201
          Making a Triple Play with Triangles ..............................................................................202
          Taking a Fourth Side with Quadrilaterals.....................................................................205
          Getting Around with Circle Measurements ..................................................................210
          Building Solid Measurement Skills ................................................................................212
          Answers to Problems in Shaping Up with Geometry ..................................................217

    Chapter 13: Getting Graphic: Cartesian Graphs ......................................................221
          Getting the Point of the Cartesian Graph .....................................................................221
          Drawing the Line on the Cartesian Graph ....................................................................225
          Answers to Problems in Getting Graphic: Cartesian Graphs.....................................228


Part IV: The X Factor: Introducing Algebra..............................233
    Chapter 14: Expressing Yourself with Algebraic Expressions.............................235
          Plug It In: Evaluating Algebraic Expressions ................................................................236
          Knowing the Terms of Separation .................................................................................237
          Adding and Subtracting Similar Terms .........................................................................239
          Multiplying and Dividing Terms.....................................................................................240
xii   Basic Math & Pre-Algebra Workbook For Dummies

                     Simplifying Expressions by Combining Similar Terms ...............................................242
                     Simplifying Expressions with Parentheses...................................................................244
                     FOILing: Dealing with Two Sets of Parentheses...........................................................245
                     Answers to Problems in Expressing Yourself with Algebraic Expressions ..............248

               Chapter 15: Finding the Right Balance: Solving Algebraic Equations................255
                     Solving Simple Algebraic Equations..............................................................................255
                     Equality for All: Using the Balance Scale to Isolate x..................................................258
                     Switching Sides: Rearranging Equations to Isolate x ..................................................259
                     Barring Fractions: Cross-Multiplying to Simplify Equations ......................................261
                     Answers to Problems in Finding the Right Balance: Solving
                       Algebraic Equations.....................................................................................................264


          Part V: The Part of Tens.........................................................271
               Chapter 16: Ten Alternative Numeral and Number Systems ................................273
                     Tally Marks .......................................................................................................................273
                     Bundled Tally Marks........................................................................................................274
                     Egyptian Numerals ..........................................................................................................274
                     Babylonian Numerals ......................................................................................................275
                     Ancient Greek Numerals .................................................................................................275
                     Roman Numerals .............................................................................................................276
                     Mayan Numerals ..............................................................................................................276
                     Base 2, or Binary Numbers.............................................................................................277
                     Base 16, or Hexadecimal Numbers................................................................................278
                     Prime-Based Numbers ....................................................................................................279

               Chapter 17: Ten Curious Types of Numbers..............................................................281
                     Square Numbers ..............................................................................................................281
                     Triangular Numbers ........................................................................................................282
                     Cubic Numbers ................................................................................................................283
                     Factorial Numbers ...........................................................................................................283
                     Powers of Two..................................................................................................................284
                     Perfect Numbers ..............................................................................................................284
                     Amicable Numbers ..........................................................................................................285
                     Prime Numbers ................................................................................................................285
                     Mersenne Primes .............................................................................................................286
                     Fermat Primes ..................................................................................................................286


          Index....................................................................................287

				
DOCUMENT INFO